Atkin-Lehner |
2- 17- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
51136l |
Isogeny class |
Conductor |
51136 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
6144 |
Modular degree for the optimal curve |
Δ |
869312 = 26 · 172 · 47 |
Discriminant |
Eigenvalues |
2- -2 0 2 -4 2 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-68,190] |
[a1,a2,a3,a4,a6] |
Generators |
[21:92:1] |
Generators of the group modulo torsion |
j |
551368000/13583 |
j-invariant |
L |
4.3003465531804 |
L(r)(E,1)/r! |
Ω |
2.8036322100074 |
Real period |
R |
3.0676966385353 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000037 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51136p1 25568e2 |
Quadratic twists by: -4 8 |